Question: The sum of two numbers is $60$, and their difference is $14$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 60}$ ${x-y = 14}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 74 $ $ x = \dfrac{74}{2} $ ${x = 37}$ Now that you know ${x = 37}$ , plug it back into $ {x+y = 60}$ to find $y$ ${(37)}{ + y = 60}$ ${y = 23}$ You can also plug ${x = 37}$ into $ {x-y = 14}$ and get the same answer for $y$ ${(37)}{ - y = 14}$ ${y = 23}$ Therefore, the larger number is $37$, and the smaller number is $23$.